Aftertreatment device NOx conversion efficiency diagnostics using on board adaptive diagnostic algorithm

ABSTRACT

A powertrain includes an internal combustion engine and an aftertreatment system having an aftertreatment device utilizing a catalyst to convert NOx. A method for indicating a malfunctioning catalyst includes monitoring an actual NOx content exiting the aftertreatment system, monitoring factors affecting conversion efficiency of the aftertreatment device, determining a predicted threshold NOx content exiting the aftertreatment system for an exemplary malfunctioning catalyst based upon the factors affecting conversion efficiency, comparing the actual NOx content exiting the aftertreatment system to the predicted threshold NOx content exiting the aftertreatment system, and indicating a malfunctioning catalyst based upon the comparing.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional Application No.61/090,041 filed on Aug. 19, 2008 which is hereby incorporated herein byreference.

TECHNICAL FIELD

This disclosure is related to control of aftertreatment of NOx emissionsin internal combustion engines.

BACKGROUND

The statements in this section merely provide background informationrelated to the present disclosure and may not constitute prior art.

Emissions control is an important factor in engine design and enginecontrol. NOx, is a known by-product of combustion. NOx is created bynitrogen and oxygen molecules present in engine intake airdisassociating in the high temperatures of combustion, and rates of NOxcreation include known relationships to the combustion process, forexample, with higher rates of NOx creation being associated with highercombustion temperatures and longer exposure of air molecules to thehigher temperatures. Reduction of NOx created in the combustion processand management of NOx in an exhaust aftertreatment system are prioritiesin vehicle design.

NOx molecules, once created in the combustion chamber, can be convertedback into nitrogen and oxygen molecules in exemplary devices known inthe art within the broader category of aftertreatment devices. However,one having ordinary skill in the art will appreciate that aftertreatmentdevices are largely dependent upon operating conditions, such as deviceoperating temperature driven by exhaust gas flow temperatures.

Modern engine control methods utilize diverse operating strategies tooptimize combustion. Some operating strategies, optimizing combustion interms of fuel efficiency, include lean, localized, or stratifiedcombustion within the combustion chamber in order to reduce the fuelcharge necessary to achieve the work output required of the cylinder.While temperatures in the combustion chamber can get high enough inpockets of combustion to create significant quantities of NOx, theoverall energy output of the combustion chamber, in particular, the heatenergy expelled from the engine through the exhaust gas flow, can begreatly reduced from normal values. Such conditions can be challengingto exhaust aftertreatment strategies, since, as aforementioned,aftertreatment devices frequently require an elevated operatingtemperature, driven by the exhaust gas flow temperature, to operateadequately to treat NOx emissions.

Aftertreatment devices are known, for instance, utilizing catalystscapable of storing some amount of NOx, and engine control technologieshave been developed to combine these NOx traps or NOx adsorbers withfuel efficient engine control strategies to improve fuel efficiency andstill achieve acceptable levels of NOx emissions. One exemplary strategyincludes using a lean NOx trap to store NOx emissions during fuel leanoperations and then purging the stored NOx during fuel rich, highertemperature engine operating conditions with conventional three-waycatalysis to nitrogen and water. Such purging events or regenerationevents can be the result of changing vehicle operation or forced purgingevents. A forced purging event requires monitoring the amount of NOxstored and some mechanism or criteria to initiate the purge. Forexample, a NOx trap has a limited storage capacity, and sensors can beused in the exhaust gas flow to estimate NOx creation in order toestimate the NOx trap state. Once the NOx trap gets close to its fullcapacity, it must be regenerated with a fuel rich reducing “pulse”. Itis desirable to control the efficiency of the regeneration event of theNOx trap to provide optimum emission control and minimum fuelconsumption. Various strategies have been proposed.

Techniques are known for adsorbing NOx (trapping) when the air-fuelratio of the exhaust gas flowing into the NOx adsorbent is lean andreleasing the adsorbed NOx (regenerating) when the air-fuel ratio of theexhaust gas flowing into the NOx adsorbent becomes rich wherein theamount of NOx adsorbed in the NOx adsorbent may be estimated from theengine load and the engine rotational speed. When the amount of theestimated NOx becomes the maximum NOx adsorption capacity of the NOxadsorbent, the air-fuel ratio of the exhaust gas flowing into the NOxadsorbent is made rich. Determination of a regeneration phase may alsobe on the basis of individual operating cycles of the internalcombustion engine.

It is also known to estimate how full the NOx trap is by estimating theamount of NOx flowing into the NOx trap using a NOx sensor or a pre-NOxtrap oxygen sensor. It is also known to schedule regeneration based onestimations of accumulated NOx mass and engine load and speed operatingcondition probabilities.

Increasingly stringent emission standards require NOx aftertreatmentmethods, utilizing, for example, a selective catalytic reduction device(SCR). An SCR utilizes ammonia derived from urea injection or recoveredfrom normal operation of a three-way catalyst device to treat NOx.Additionally, it is known to operate a diesel oxidation catalyst (DOC)upstream of the SCR in diesel applications to convert NO into NO₂preferable to treatment in the SCR. Continued improvement in exhaustaftertreatment requires accurate information regarding NOx emissions inthe exhaust gas flow in order to achieve effective NOx reduction, suchas dosing proper amount of urea based on monitored NOx emissions.

Aftertreatment devices such as lean NOx traps and SCRs convert NOx toother constituents at some conversion efficiency. Conversion efficiencycan be described by the flow of NOx flowing into a device versus theflow of NOx exiting the device. An aftertreatment device operatingproperly experiences reduced efficiency according to properties of theexhaust gas flow that affect the chemical reaction occurring in thedevice. For example, temperature and space velocity of the gases withina NOx trap affect the efficiency of the device. Temperature and spacevelocity of the gases within an SCR device similarly affect theefficiency of the device. These environmental factors can be monitoredin the aftertreatment system, and effects of these factors upon deviceconversion efficiency can be estimated. Additionally, malfunctions ordegraded performance caused by wear or damage can reduce the efficiencyof the aftertreatment device. A method to distinguish degradedperformance based upon transient environmental conditions from amalfunctioning or damaged aftertreatment device would be beneficial todiagnosing a malfunction condition in the device.

SUMMARY

A powertrain includes an internal combustion engine and anaftertreatment system having an aftertreatment device utilizing acatalyst to convert NOx. A method for indicating a malfunctioningcatalyst includes monitoring an actual NOx content exiting theaftertreatment system, monitoring factors affecting conversionefficiency of the aftertreatment device, determining a predictedthreshold NOx content exiting the aftertreatment system for an exemplarymalfunctioning catalyst based upon the factors affecting conversionefficiency, comparing the actual NOx content exiting the aftertreatmentsystem to the predicted threshold NOx content exiting the aftertreatmentsystem, and indicating a malfunctioning catalyst based upon thecomparing.

BRIEF DESCRIPTION OF THE DRAWINGS

One or more embodiments will now be described, by way of example, withreference to the accompanying drawings, in which:

FIG. 1 schematically depicts an exemplary diesel engine, in accordancethe present disclosure;

FIG. 2 schematically depicts an exemplary aftertreatment system, inaccordance with the present disclosure;

FIG. 3 graphically illustrates exemplary test data relating conversionefficiency to catalyst bed temperature and space velocity in anexemplary SCR, in accordance with the present disclosure;

FIG. 4 illustrates an exemplary information flow diagnosing amalfunction catalyst through methods described herein, in accordancewith the present disclosure;

FIG. 5 schematically depicts an exemplary NOx model module, utilizedwithin an engine control module and determining an NOx creationestimate, in accordance with the present disclosure;

FIG. 6 graphically illustrates an exemplary mass fraction burn curve inaccordance with the present disclosure;

FIG. 7 graphically illustrates an exemplary cylinder pressure plottedagainst crank angle through a combustion process, in accordance with thepresent disclosure;

FIG. 8 depicts a number of different temperatures capable of estimationwithin the combustion chamber important to describing the combustionprocess, in accordance with the present disclosure;

FIG. 9 is a graphical depiction of exemplary modeled results describingstandardized effects of a number of inputs to NOx emissions under agiven set of conditions, in accordance with the present disclosure;

FIG. 10 graphically illustrates exemplary data, comparing predicted NOxexiting an aftertreatment system generated according to noisy inputdata, in accordance with the present disclosure; and

FIG. 11 graphically illustrates exemplary data processed through anintegration calculation, in accordance with the present disclosure.

DETAILED DESCRIPTION

Referring now to the drawings, wherein the showings are for the purposeof illustrating certain exemplary embodiments only and not for thepurpose of limiting the same, FIG. 1 is a sectional representation of anexemplary diesel engine, in accordance with the present disclosure.Engine 10 conventionally includes a plurality of cylinders 12 havingtherein reciprocable pistons 14 connected with a crankshaft 16. Thisdisclosure is generally applicable to direct injection four-strokecompression ignition engines. The ends of the cylinder are closed by acylinder head 18 so that the cylinders and pistons define variablevolume combustion chambers 20.

The cylinder head is provided with intake valves 22 which control thetiming and flow of intake air into the cylinders during intake strokesof the pistons. Exhaust valves 24 in the cylinder head control timingand flow of exhaust products from the combustion chambers during exhauststrokes of the pistons. In the engine shown there are two intake valvesand two exhaust valves for each cylinder, however, any suitable numberof valves provided for operation of the engine may be utilized inaccordance with the disclosure.

The intake and the exhaust valves are actuated by separate valveactuation devices 26, 28. The valve actuation devices exclusivelyoperate their respective intake and exhaust valves, however, both aredriven by the crankshaft 16 through a timing chain 30.

The exemplary engine 10 includes a cast-metal engine block with aplurality of cylinders formed therein and an engine head. The engineblock preferably includes coolant passages 32 through which enginecoolant fluid passes. A coolant temperature sensor, operable to monitortemperature of the coolant fluid, is located at an appropriate location,and provides a signal input to a control system indicative of engineoperating temperature useful in engine control. The engine preferablyincludes known systems including an external exhaust gas recirculation(EGR) valve and an intake air throttle valve (not shown).

Each piston 14 is connected via a pin and connecting rod to thecrankshaft 16. The crankshaft 16 is rotatably attached to the engineblock at a main bearing area near a bottom portion of the engine block,such that the crankshaft is able to rotate around an axis that isperpendicular to a longitudinal axis defined by each cylinder. A cranksensor (not shown) is placed in an appropriate location, operable togenerate a signal that is useable by the controller to measure crankangle, and which is translatable to provide measures of crankshaftrotation, speed, and acceleration that are useable in various controlschemes. During operation of the engine, each piston 14 moves up anddown in the cylinder in a reciprocating fashion due to connection to androtation of the crankshaft 16, and the combustion process. The rotationaction of the crankshaft effects translation of linear force exerted oneach piston during combustion to an angular torque output from thecrankshaft, which can be transmitted to another device, e.g. a vehicledriveline.

The engine head comprises a cast-metal device having one or more intakeports and one or more exhaust ports which flow to the combustion chamber20. The intake port supplies air to the combustion chamber 20. Combusted(burned) gases flow from the combustion chamber 20 via the exhaust port.Flow of air through each intake port is controlled by actuation of oneor more intake valves 22. Flow of combusted gases through each exhaustport is controlled by actuation of one or more exhaust valves 24.

The intake and exhaust valves 22, 24 each have a head portion thatincludes a top portion that is exposed to the combustion chamber. Eachof the valves 22, 24 has a stem that is connected to a valve actuationdevice. A valve actuation device 26 is operative to control opening andclosing of each of the intake valves 22, and a second valve actuationdevice 28 operative to control opening and closing of each of theexhaust valves 24. Each of the valve actuation devices 26, 28 comprisesa device signally connected to the control system and operative tocontrol timing, duration, and magnitude of opening and closing of eachvalve, either in concert or individually. One embodiment of theexemplary engine comprises a dual overhead cam system which has variablelift control (VLC) and variable cam phasing (VCP) devices as part of thevalve actuation devices 26, 28. VCP devices are operative to controltiming of opening or closing of each intake valve and each exhaust valverelative to rotational position of the crankshaft and opens each valvefor a fixed crank angle duration. VLC devices are operative to controlmagnitude of valve lift to one of two positions: one position to 3-5 mmlift for an open duration of 120-150 crank angle degrees, and anotherposition to 9-12 mm lift for an open duration of 220-260 crank angledegrees. Individual valve actuation devices can serve the same functionto the same effect. The valve actuation devices are preferablycontrolled by the control system according to predetermined controlschemes. Alternative variable valve actuation devices including, forexample, fully flexible electrical or electro-hydraulic devices may alsobe used and have the further benefit of independent opening and closingphase control as well as substantially infinite valve lift variabilitywithin the limits of the system. A specific aspect of a control schemeto control opening and closing of the valves is described herein.

Air is inlet to the intake port through an intake manifold runner 34,which receives filtered air passing through a known air metering deviceand a throttle device (not shown). Exhaust gas passes from the exhaustport to an exhaust manifold, which includes exhaust gas sensorsoperative to monitor constituents of the exhaust gas flow, and determineparameters associated therewith. The exhaust gas sensors can compriseany of several known sensing devices operative to provide values for theexhaust gas flow, including air/fuel ratio, or measurement of exhaustgas constituents, e.g. NOx, CO, HC, and others. The system may includean in-cylinder sensor for monitoring combustion pressures, ornon-intrusive pressure sensors or inferentially determined pressuredetermination (e.g. through crankshaft accelerations). Theaforementioned sensors and metering devices each provide a signal as aninput to the control system. These inputs can be used by the controlsystem to determine combustion performance measurements.

The control system preferably comprises a subset of an overall controlarchitecture operable to provide coordinated system control of theengine 10 and other systems. In overall operation, the control system isoperable to synthesize operator inputs, ambient conditions, engineoperating parameters, and combustion performance measurements, andexecute algorithms to control various actuators to achieve targets forcontrol parameters, including such parameters as fuel economy,emissions, performance, and drivability. The control system is operablyconnected to a plurality of devices through which an operator controlsor directs operation of the engine. Exemplary operator inputs include anaccelerator pedal, a brake pedal, transmission gear selector, andvehicle speed cruise control when the engine is employed in a vehicle.The control system may communicate with other controllers, sensors, andactuators via a local area network (LAN) bus (not shown) whichpreferably allows for structured communication of control parameters andcommands between various controllers.

The control system is operably connected to the engine 10, and functionsto acquire data from sensors, and control a variety of actuators of theengine 10 over appropriate interfaces. The control system receives anengine torque command, and generates a desired torque output, based uponthe operator inputs. Exemplary engine operating parameters that aresensed by control system using the aforementioned sensors include enginecoolant temperature, crankshaft rotational speed (RPM) and position,manifold absolute pressure, ambient air flow and temperature, andambient air pressure. A sensor capable of monitoring crankshaftrotational position can be utilized to monitor or determine aprogression of the engine and various cylinders through various stagesof a combustion cycle. Combustion performance measurements may comprisemeasured and inferred combustion parameters, including air/fuel ratio,location of peak combustion pressure, among others.

Actuators controlled by the control system include: fuel injectors (notshown); the VCP/VLC valve actuation devices 26, 28; EGR valve (notshown), and, electronic throttle control module (not shown). Fuelinjectors are preferably operable to inject fuel directly into eachcombustion chamber 20.

The control system preferably comprises a general-purpose digitalcomputer generally including a microprocessor or central processingunit, read only memory (ROM), random access memory (RAM), electricallyprogrammable read only memory (EPROM), high speed clock, analog todigital (A/D) and digital to analog (D/A) circuitry, and input/outputcircuitry and devices (I/O) and appropriate signal conditioning andbuffer circuitry. Each controller has a set of control algorithms,comprising resident program instructions and calibrations stored in ROM.

Algorithms for engine control may be executed during preset loop.Algorithms stored in the non-volatile memory devices are executed by thecentral processing unit and are operable to monitor inputs from thesensing devices and execute control and diagnostic routines to controloperation of the engine, using preset calibrations. Loop cycles may beexecuted at regular intervals, for example each 3.125, 6.25, 12.5, 25and 100 milliseconds during ongoing engine operation. Alternatively,algorithms may be executed in response to occurrence of an event orinterrupt request.

FIG. 1 describes an exemplary diesel engine. However, it will beappreciated that NOx treatment and aftertreatment systems are utilizedin other engine configurations including gasoline engines, and thedisclosure is not intended to be limited to the specific exemplaryengine embodiment described herein.

FIG. 2 schematically illustrates an exemplary aftertreatment system, inaccordance with the present disclosure. Aftertreatment system 200comprises DOC 210, SCR 220, upstream NOx sensor 230, downstream NOxsensor 240, temperature sensor 250, and urea dosing module 260. DOC 210performs a number of catalytic functions necessary to aftertreatment ofan exhaust gas flow. One of the functions of DOC 210 is to convert NO, aNOx form not easily treated in an SCR, into NO₂, a NOx form easilytreated in an SCR. SCR 220 utilizes urea as a reactant to reduce NOxinto other constituents. Upstream NOx sensor 230 detects and quantifiesNOx in the exhaust gas flow entering aftertreatment system 200. Whileupstream NOx sensor 230 is illustrated as an exemplary means to quantifyNOx entering the aftertreatment system, it should be noted that NOxentering the system can be quantified for use in evaluating conversionefficiency in an SCR by other means, for example, through a NOx sensorlocated between DOC 210 and SCR 220 or through a virtual NOx sensormodeling engine output and conditions within the exhaust gas flow toestimate the presence of NOx entering the aftertreatment system. Thisdisclosure in general discusses a sensor input describing NOx enteringthe aftertreatment system in accordance with the exemplary embodiment,however it will be appreciated that, depending upon upstream sensorplacement, the input could actually describe NOx content entering aportion of the aftertreatment system. SCR 220 utilizes ammonia, forexample, as derived from injected urea, to convert NOx to otherconstituents by methods known in the art. Temperature sensor 250 isdepicted, located in a region to gather exhaust gas flow temperatureswithin the aftertreatment system 200. Urea dosing module 260 is depictedin a position upstream of SCR 220. The urea can be directly sprayed intothe exhaust gas flow entering the SCR. However, a preferred method isdepicted, utilizing a mixer device 270. Urea dosing module 260 injectsurea onto mixer device 270, and the urea is then carried by the exhaustgas flow in a substantially even distribution onto the catalyst surfaceson the interior of SCR 220. Downstream NOx sensor 240 detects andquantifies NOx in the exhaust gas flow exiting aftertreatment system200. A method is disclosed to utilize a measure of the NOx entering theaftertreatment system and a measure of the NOx exiting theaftertreatment system to determine the conversion efficiency of the NOxinto other constituents within aftertreatment devices.

Conversion efficiency is described as the efficiency with which anaftertreatment device can convert NOx into other constituents. Theexemplary aftertreatment system described above describes a measured orestimated NOx content of the exhaust gas flow measured upstream of theaftertreatment device being analyzed. This measure of NOx entering theaftertreatment system can be described at any time t as x(t). Theexemplary aftertreatment system described above describes a measured orestimated NOx content of the exhaust gas flow measured downstream of theaftertreatment device being analyzed. This measure of NOx exiting theaftertreatment system can be described at any time as y(t). Conversionefficiency at any given time by the following equation:

$\begin{matrix}{{\eta_{ACTUAL}(t)} = {1 - \frac{y(t)}{x(t)}}} & \lbrack 1\rbrack\end{matrix}$It will be appreciated that this equation provides the conversionefficiency at any instant in time. Such instantaneous measurements orcalculations are prone to error based upon signal noise. Methods toapply a low pass filter are known in the art. An integration of x(t) ory(t) yields a description of a quantity of actual NOx to enter or exitthe aftertreatment system through a time period, respectively. Anexemplary equation to determine an integrated conversion efficiency,filtering anomalous measurements in x(t) and y(t), can be described asfollows:

$\begin{matrix}{\eta_{ACTUAL} = {1 - \frac{\int{{y(t)}*{\mathbb{d}t}}}{\int{{x(t)}*{\mathbb{d}t}}}}} & \lbrack 2\rbrack\end{matrix}$In this way, measured or estimated values of NOx entering and exitingthe aftertreatment system can be utilized to determine an estimated orcalculated actual conversion efficiency of the aftertreatment system.

A properly operating or fresh aftertreatment device operates with somemaximum achievable conversion efficiency for a given set of conditions.However, it will be appreciated that aftertreatment devices,particularly devices utilizing a catalyst, are subject to degradedperformance over time and in particular with exposure to hightemperatures.

Conversion efficiency in a fresh device is affected by a number ofenvironmental or operational factors. Conversion efficiency for anexemplary SCR can be determined by a model expressed by the function:η=f(T _(BED),SV,θ_(NH) ₃ ,x(t),V _(UREA),ρ_(CELL))  [3]T_(BED) describes the temperature of the catalyst bed within the SCR.This temperature can be directly measured or can be estimated based upontemperature, flow rate, and other properties of the exhaust gas flow. SVdescribes the surface velocity of exhaust gas flowing through the SCRdevice and can be determined as a function of properties of the exhaustgas flow, including temperature and flow rate. θ_(NH) ₃ describes anamount of ammonia storage on the catalyst bed, and adequate presence ofammonia on the SCR is required to achieve the desired NOx conversionreaction. θ_(NH) ₃ can be estimated, for example, by analyzing ammoniaadsorbtion and desorbtion rates, NOx conversion rates, and adsorbedammonia oxidation rates. As described above, x(t) describes the presenceof NOx in the exhaust gas flow entering the aftertreatment system. Lowlevels of NOx are easily reacted within a properly functioning SCR,while levels of NOx above a certain threshold are more difficult toreact and correspond to lower conversion efficiencies. An example of afactor limiting treatment of NOx above certain quantities includeslimited ammonia present in an SCR. V_(UREA) describes the volume of ureainjected. While V_(UREA) describes a presence of ammonia similarly toθ_(NH) ₃ , V_(UREA) includes a present measure of urea being injectedand can better describe transient indicator for ammonia expected to bepresent in the near future. ρ_(CELL) describes the density of catalystmaterial within the SCR and, therefore, describes a capacity of the SCRto catalyze the intended reaction.

The above model describing conversion efficiency includes factors whichcan be assumed or confirmed in normal operation of an SCR. As a result,the model can be simplified, thereby reducing a processing load requiredto analyze conversion efficiency through the model. For example, aV_(UREA) can be monitored through operation of the urea dosing module,and given V_(UREA) values in a particular intended range, the resultingconversion efficiency calculations should remain unaffected. In someembodiments, V_(UREA) is controlled to be substantially directlyproportional to x(t). Additionally, θ_(NH) ₃ can in some embodiments beestimated based upon V_(UREA), monitored characteristics of the exhaustgas flow and of the SCR, such as temperature, and x(t). Given θ_(NH) ₃values in a normal range, θ_(NH) ₃ can be reduced to a portion of thefunctional model dependent upon T_(BED). A value for x(t), as describedabove, can be monitored through an upstream NOx sensor or a virtual NOxsensor. ρ_(CELL) is a characteristic of the SCR device and is a knownvalue. As a result of these known or estimable factors, a nominalconversion efficiency for an exemplary fresh or ideal SCR can bedetermined by a model expressed by the function:η_(NO) =f(T _(BED),SV,θ_(NH) ₃ )  ([4]In this way, conversion efficiency of the SCR can be accuratelydetermined as an on board diagnostic function by maintaining otherfactors within known or calibrated ranges.

The above factors are used to describe or estimate conversion efficiencyof the chemical reaction taking place within the SCR. It will beappreciated that similar expressions can be utilized to describeconversion reactions occurring within other aftertreatment devices. Forexample, a lean NOx trap with known geometric and catalytic properties,depending primarily upon a temperature within the device and the speedat which exhaust gas is flowing through the device, operates inregeneration cycles to convert adsorbed NOx into other constituents. Anominal conversion efficiency for an exemplary fresh lean NOx can bedetermined by a model expressed by the following function:η_(NO) =f(T _(BED),SV)  [5]Because a lean NOx trap does not depend upon injection of any reactant,such as urea in an SCR, conversion efficiency of the lean NOx trap canbe accurately determined as an on board diagnostic function bymonitoring temperature and space velocity.

Based upon the above models or other models known in the art for aparticular aftertreatment device, a conversion efficiency for a freshaftertreatment device can be estimated or predicted. A malfunctionconversion efficiency for a device under given operating conditions canbe calibrated based upon test data or can be set as a fraction of anestimated conversion efficiency of a fresh device. A degree of degradedconversion efficiency indicating that the aftertreatment device is notoperating properly may be developed experimentally, empirically,predictively, through modeling or other techniques adequate toaccurately predict aftertreatment device operation, and a multitude ofmalfunction conversion efficiencies might be used by the sameaftertreatment device for different conditions or operating ranges.Subject to the assumptions described above, a malfunction conversionefficiency (η_(malf) _(—) _(predicted)) for an SCR can be expressed bythe following function:η_(malf) _(—) _(predicted) =f(T _(BED),SV,θ_(NH) ₃ )  [6]In this case, the malfunction conversion efficiency can be expressed asa function of the temperature within the device, the speed of theexhaust gases flowing through the device, and the amount of ammoniastorage. A similar η_(malf) _(—) _(predicted) term for a lean NOx trapcan be described by the following equation:η_(malf) _(—) _(predicted) =f(T _(BED) ,SV)  [7]Such functions can be defined or mapped by test data or calibratedvalues known to indicate a malfunction catalyst for given inputconditions. Such a functional relationship can be available within thevehicle as a look-up table stored in device memory, a computerized modelbased upon the functional relationship, or any other method known in theart. Alternatively, given a known acceptable or nominal conversionefficiency that should result from within a fresh device (η_(NO)) undercurrent conditions, a calibratable threshold factor (A) can be utilizedto indicate a malfunction in the device. An exemplary equation that canbe utilized to describe a malfunction conversion efficiency is expressedby the following:1−η_(malf) _(—) _(predicted) =A*(1−η_(NO))  [8]Solving this equation for η_(malf) _(—) _(predicted) yields thefollowing equation:η_(malf) _(predicted)=1−A*(1−η_(NO))  [9]A can be dynamically set during operation of the powertrain based uponfactor affecting conversion efficiency in the aftertreatment device. Anexemplary method to set A can set the value based upon SV and T_(BED). Avalue for A can be calculated utilizing a functional relationship duringoperation, or a value can be determined from a look-up table based uponpredetermined calculations or data. Using either of the above exemplarymethods, a malfunction conversion efficiency can be utilized todetermine a conversion efficiency value indicating a malfunction in anaftertreatment device under a set of operating conditions.

The above methods utilize a malfunction conversion efficiency toindicate a malfunction catalyst. It will be appreciated that a similarmethod can be utilized according to a nominal efficiency and a decreasedefficiency term, avoiding the use of a malfunction efficiency term.However, one will appreciate that such a method is a simplerearrangement of Equation 8, solving for the difference between theη_(NO) and η_(malf) _(—) _(predicted) terms. In this way, predictivemethods described herein can be utilized to indicate a malfunctioncatalyst by determining the difference between η_(NO) and η_(ACTUAL) andindicating the malfunction catalyst if the difference is more than adetermined threshold.

FIG. 3 graphically illustrates exemplary test data relating conversionefficiency to catalyst bed temperature and space velocity in anexemplary SCR, in accordance with the present disclosure. Thethree-dimensionally projected surface describes conversion efficiencywithin an exemplary fresh SCR. In a two-dimensional plane wherein SVequals one, an exemplary data curve is depicted illustrating behavior ofa malfunction catalyst. Utilizing such test data or exemplary datagathered in a vehicle through normal operation, a comparison of measuredconversion efficiency to nominal conversion efficiency can yield adetermination of a malfunction catalyst within an aftertreatment device.

As described above an integration of x and y terms can utilized to applya low pass filter in determining an actual conversion efficiency. Asimilar method can be employed in determining a malfunction conversionefficiency. Utilizing a known or predicted behavior of a device,utilizing data such as described in FIG. 3 to generate a predictedmalfunction conversion efficiency, and monitoring an x(t) input, apredicted y_(malf)(t) can be described based upon current operatingconditions. An exemplary embodiment of an equation describing thisprediction can be expressed as follows:y _(malf)(t)=(1−η_(malf) _(—) _(predicted))*x(t)  [10]By integrating this term through a time period, a threshold total NOxexiting the aftertreatment can be described as ∫y_(malf)(t)*dt. Bycomparing measured or actual NOx exiting from the aftertreatment systemto this threshold term, an indication of a malfunction catalyst can beperformed. Additionally, a filtered η_(malf) _(—) _(predicted) term canbe determined. This calculation can be expressed as follows:

$\begin{matrix}{\eta_{{{malf}\_{predicted}}{\_{filtered}}} = {1 - \frac{\int{{y_{malf}(t)}*{\mathbb{d}t}}}{\int{{x(t)}*{\mathbb{d}t}}}}} & \lbrack 11\rbrack\end{matrix}$This term yields a predicted conversion efficiency that a thresholdmalfunctioning catalyst would exhibit with given x(t) values through atime period based upon η_(malf) _(—) _(predicted) from a modelpredicting device behavior.

The above methods compare conversion efficiencies to identify amalfunction catalyst. Alternative methods are disclosed to indicate amalfunction catalyst, for example, based upon comparing a predicted NOxcontent exiting the aftertreatment system to an actual NOx contentexiting the aftertreatment system. By comparing y_(malf)(t) to y(t), anevaluation can be made at time t whether the catalyst is functioningproperly. In order to improve the estimation and filter out effects ofnoise, known methods to analyze y_(malf)(t) and y(t) can be used toevaluate the catalyst. For example, multiple comparisons of the termscan be stored and statistically analyzed. In another example, the termscan be integrated over a period of time and compared. In one exemplaryembodiment utilizing integration to compare the terms, a factor A asdescribed in association with Equation 8 can be utilized to determine aη_(malf) _(—) _(predicted) term in relation to a known η_(NO) value.This relationship can be rearranged into the following equation:

$\begin{matrix}{A = \frac{1 - \eta_{{malf}\_{predicted}}}{1 - \eta_{NO}}} & \lbrack 12\rbrack\end{matrix}$A rearrangement of Equation 9 and an equivalent expression of η_(NO) andan integration of y_(NO)(t) values, fed into Equation 10, yield thefollowing equation:

$\begin{matrix}{A = {{\frac{\int{{y_{malf}(t)}*{\mathbb{d}t}}}{\int{{x(t)}*{\mathbb{d}t}}} \div \frac{\int{{y_{NO}(t)}*{\mathbb{d}t}}}{\int{{x(t)}*{\mathbb{d}t}}}} = \frac{\int{{y_{malf}(t)}*{\mathbb{d}t}}}{\int{{y_{NO}(t)}*{\mathbb{d}t}}}}} & \lbrack 13\rbrack\end{matrix}$The term y_(NO)(t) can be estimated based upon the models described byEquations 3, 4 or 5 and x(t). Based upon Equation 13, given a calibratedA value and a predicted integration of y_(NO)(t) through a time period,a predicted threshold value for an integration of y_(malf)(t) can bedetermined describing a quantity of NOx exiting the aftertreatmentsystem in a malfunctioning catalyst (dividing ∫y_(NO)(t)*dt by A yields∫y_(malf)(t)*dt). By comparing a measure of actual NOx exiting theaftertreatment system, or ∫y(t)*dt, to a predicted threshold NOx exitingthe aftertreatment system for malfunction catalyst, or ∫y_(malf)(t)*dt,a determination can be made whether the catalyst being monitored ismalfunctioning.

As described above, methods can be employed utilizing η_(NO) and adetermined drop in conversion efficiency in place of η_(malf) _(—)_(predicted). Similarly, a method is disclosed to indicate a malfunctioncatalyst based upon comparing a y_(NO) term to a y_(ACTUAL) term, andindicating the malfunction catalyst based upon y_(ACTUAL) being greaterthan y_(NO) by more than a threshold NOx content above nominal. Thethreshold NOx content above nominal value can be developedexperimentally, empirically, predictively, through modeling or othertechniques adequate to accurately predict operation of theaftertreatment system, and value can be dynamically determined, forexample, based upon catalyst bed temperature and space velocity withinthe device. The y_(NO) term can be calculated, for example, by thefollowing equation determined similarly to Equation 10:y _(NO)(t)=(1−η_(NO))*x(t)  [14]A comparison utilizing this term can be performed using each of y_(NO)and y_(ACTUAL) integrated or filtered through a time period according tomethods described herein.

The above determinations of terms, including predicted conversionefficiency and nominal conversion efficiency, as described above, aredependent upon terms affecting conversion efficiency. Determinations canbe calculated in real time based upon programmed functionalrelationships resulting from calibration results, predictive models, orany other method sufficient to predict operation of the aftertreatmentsystem. Additionally or alternatively, some or all of the functionalrelationships can be embodied in look-up tables, wherein factorsaffecting conversion efficiency are used as inputs to the look-uptables. Other factors, such as y_(malf)(t), can similarly be calculatedor stored in look-up tables according to methods described herein.

Utilizing the above methods to determine an actual NOx exiting theaftertreatment system and to determine a predicted threshold NOx exitingthe aftertreatment system for malfunction catalyst can be utilizedtogether to diagnose a malfunction catalyst in an aftertreatment device.If the actual NOx exiting the aftertreatment system is greater than thepredicted threshold NOx exiting the aftertreatment system formalfunction catalyst for current operating conditions, then amalfunction catalyst can be indicated. FIG. 4 illustrates an exemplaryinformation flow diagnosing a malfunction catalyst through methodsdescribed herein, in accordance with the present disclosure. Informationflow 400 comprises an actual NOx determination module 410, a conversionefficiency model module 420, an integrated diagnostic threshold module430, and a comparator module 440. Actual NOx determination module 410monitors y(t), describing NOx exiting an aftertreatment system.Integrating y(t), a ∫y(t)*dt term is determined. Simultaneously,conversion efficiency model module 420 monitors inputs regarding x(t),T_(BED)(t), SV(t), and θ_(NH) ₃ (t) and applies a calibrated modeldescribing conversion efficiency η_(malf) _(—) _(predicted) for amalfunction device. η_(malf) _(—) _(predicted) can be determined bymethods described herein. A y_(malf)(t) term, describing a NOx exitingthe aftertreatment system term that would indicate a catalystmalfunction calculated according to exemplary Equation 10, is developedand output from module 420 to integrated diagnostic threshold module430. Integrated diagnostic threshold module 430 applies an integrationof y_(malt)(t) through a time period according to Equation 9 and outputsa ∫y_(malf)(t)*dt term. ∫y(t)*dt and ∫y_(malf)(t)*dt are compared incomparator module 440. If ∫y(t)*dt is less than ∫y_(malf)(t)*dt then thecatalyst is determined to be in a normal state. If ∫y(t)*dt is greaterthan ∫y_(malf)(t)*dt then the catalyst is determined to be a malfunctioncatalyst, and a malfunction indication is generated. This determinationcan be made continuously, at recurring intervals, or can be initiatedupon certain events like an engine start-up event.

The method described in association with FIG. 4 includes x(t) or ameasure of NOx entering the aftertreatment system. However, it should benoted that this term is utilized to generate an accurately predictedy_(malf)(t) term for later integration. In the event that the x(t) termis unavailable or determined to be unreliable, an alternative estimationof y_(malf)(t) or ∫y_(malf)(t)*dt can otherwise be determined forcomparison to ∫y(t)*dt. For example, a predicted threshold NOx exitingfrom the aftertreatment system could be generated based upon a look-uptable and certain engine operating characteristics detailing NOxproduction. Some of these exemplary characteristics are described belowin sections detailing operation of a virtual NOx sensor, and some or allof these factors could likewise be utilized to estimate the predictedthreshold term in lieu of a malfunctioning sensor.

A number of reactions in the vehicle can be undertaken in a vehiclewherein an aftertreatment device has been determined to bemalfunctioning. For example, a warning can be issued to the operator,instructing the operator to schedule repair or replacement of thecatalyst. A similar warning can additionally or alternatively be storedin an error log for recall by a maintenance technician or transmitted toa remote maintenance server for remote use. In another example, anindication of a malfunctioning catalyst can be used to deemphasize ordisable use of an SCR device, for example, reducing the volume of ureainjected in the device. Such a change in the use of the aftertreatmentsystem can increasingly utilize other devices in the aftertreatmentsystem or command modulation engine operation to avoid excessivebreakthrough of NOx past the SCR device or slippage of unutilizedammonia. In a system wherein more than one SCR device or catalyst isutilized or available, a malfunctioning catalyst can be deselected infavor of a remaining functional catalyst. A number of reactions to amalfunction catalyst are envisioned, and the disclosure is not intendedto be limited to the particular embodiments described herein.

A NOx sensor or an oxygen sensor add cost and mass to a vehicle, andsuch sensors frequently require a particular operating temperaturerange, achieved after some warm-up time, to be functional. As describedabove a virtual NOx sensor can be used to estimate the presence of NOxin an aftertreatment system. FIG. 7 schematically depicts an exemplaryNOx model module, utilized within an engine control module anddetermining a NOx creation estimate, in accordance with the presentdisclosure. Exemplary NOx model module 500 is operated within NOxcreation estimating system 510 and comprises a model module 520 and aNOx estimation module 530. Engine sensor inputs x₁ through x_(n) areinputs to the NOx model module and can include a number of factors,including temperatures, pressures, engine control settings includingvalve and spark timings, and other readings indicative of combustionstate within the combustion chamber. Model module 520 receives theseinputs and applies known relationships to determine a number ofparameters to describe combustion within the combustion chamber.Examples of these descriptive parameters include EGR %, the percentageof exhaust gas diverted back into the combustion chamber in order tocontrol the control the combustion process; an air-fuel charge ratio(AFR) describing the mixture of air and fuel present in the combustionchamber; combustion temperature measurables, including, for example,either combustion burned gas temperature or average combustiontemperature; a combustion timing measurable tracking the progress ofcombustion through a combustion process, for example CA50, a measurementof at what crank angle 50% of the mass of fuel originally present in thecombustion chamber is combusted; and fuel rail pressure, indicating thepressure of fuel available to fuel injectors to be sprayed into thecombustion chamber. These descriptive parameters can be used to estimateconditions present within the combustion chamber through the combustionprocess. As described above, conditions present within the combustionchamber affect the creation of NOx in the combustion process. Thesedescriptive parameters can be fed to NOx estimation module 530, whereinprogrammed calculations utilize the descriptive parameters as inputs togenerate an estimate of NOx creation due to the combustion process.However, as described above, models analyzing variable descriptive ofthe combustion process can include complex calculations which can takelonger to calculate than required for generating real-time results,require large amounts of processing capability, and are only as accurateas the pre-programmed algorithm permits. As a result of these challengesand a need for accurate and timely information, estimation of NOxcreation within an ECM as part of an aftertreatment control strategy isnot preferable.

A variety of engine sensor inputs can be used to quantify parametersdescriptive of the combustion process. However, combustion occurringwithin the engine is difficult to directly monitor. Sensors may detectand measure fuel flow and air flow into the cylinder, a sensor maymonitor a particular voltage being applied to a spark plug or aprocessor may gather a sum of information that would predict conditionsnecessary to generate an auto-ignition, but these readings together aremerely predictive of combustion and do not measure actual combustionresults. One exemplary method measuring actual combustion resultsutilizes pressure measurements taken from within the combustion chamberthrough a combustion process. Cylinder pressure readings providetangible readings describing conditions within the combustion chamber.Based upon an understanding of the combustion process, cylinderpressures may be analyzed to estimate the state of the combustionprocess within a particular cylinder, describing the combustion in termsof both combustion phasing and combustion strength. Combustion of aknown charge at known timing under known conditions produces apredictable pressure within the cylinder. By describing the phase andthe strength of the combustion at certain crank angles, the initiationand the progression of a particular combustion process may be describedas an estimated state of combustion. By estimating the state of thecombustion process for a cylinder, factors affecting NOx creationthrough the combustion process can be determined and made available foruse in NOx creation estimation.

One known method for monitoring combustion phasing is to estimate themass fraction burn ratio for a given crank angle based upon knownparameters. The mass fraction burn ratio describes what percentage ofthe charge in the combustion chamber has been combusted and serves as agood estimate of combustion phasing. FIG. 6 graphically illustrates anexemplary mass fraction burn curve in accordance with the presentdisclosure. For a given crank angle, the curve depicted describes theestimated percentage of fuel air mixture within the charge that has beencombusted for that combustion process. In order to be used as a metricof combustion phasing, it is known to identify either a particular massfraction burn percentage of interest or a particular crank angle ofinterest. FIG. 6 identifies CA50% as a crank angle at which the massfraction burn equals 50%. By examining this particular metric across aplurality of combustion processes in this cylinder or across a number ofcylinders, the comparative phasing of the particular combustionprocesses may be described.

As described above, combustion phasing can be utilized to estimate thestate of a particular combustion process. An exemplary method formonitoring combustion phasing to diagnose ineffective combustion isdisclosed whereby combustion in an engine is monitored, mass fractionburn ratios are generated for each cylinder combustion process, and thecombustion phasing across the cylinders are compared. If the combustionphase for one cylinder at a particular crank angle for that firstcylinder differs by more than a threshold phase difference from thecombustion phase for another cylinder at the same crank angle for thatsecond cylinder, anomalous combustion can be inferred. Many sources ofanomalous combustion may be diagnosed by this method. For example, ifsome condition causes early ignition or knocking within the combustionchamber, the cylinder pressure readings will exhibit different valuesthan normal combustion. Additionally, fuel system injection timingfaults, causing injection of the charge at incorrect timing, will causeanomalous cylinder pressure readings. Further, if a cylinder misfires ornever achieves combustion, the cylinder pressure readings will exhibitdifferent values than normal combustion. Similarly, pressure curves maybe used to diagnose other abnormal combustion conditions, such aschanges in the air fuel mixture, changes in camshaft phasing, andmaintenance failures to related components. Any such diagnoses ofcombustion health have implications to NOx and can be useful to estimateNOx creation.

Many methods are known to estimate mass fraction burn. One methodexamines pressure data from within the combustion chamber, includinganalyzing the pressure rise within the chamber attributable tocombustion. Various methods exist to quantify pressure rise in acylinder attributable to combustion. Pressure ratio management (PRM) isa method based upon the Rassweiler approach, which states that massfraction burn may be approximated by the fractional pressure rise due tocombustion. Combustion of a known charge at a known time under knownconditions tends to produce a consistently predictable pressure risewithin the cylinder. PRM derives a pressure ratio (PR) from the ratio ofa measured cylinder pressure under combustion at a given crank angle(PCYL(θ)) to a calculated motored pressure, estimating a pressure valueif no combustion took place in the cylinder, at a given crank angle(PMOT(θ)), resulting in the following equation:

$\begin{matrix}{{P\;{R(\theta)}} = \frac{P_{CYL}(\theta)}{P_{MOT}(\theta)}} & \lbrack 15\rbrack\end{matrix}$FIG. 7 graphically illustrates an exemplary cylinder pressure plottedagainst crank angle through a combustion process, in accordance with thepresent disclosure. P_(MOT)(θ) exhibits a smooth, inverse parabolic peakfrom the piston compressing a trapped pocket of gas without anycombustion. All valves are closed with the piston at BDC, the pistonrises compressing the gas, the piston reaches TDC at the peak of thepressure curve, and the pressure reduces as the piston falls away fromTDC. A rise in pressure above P_(MOT)(θ) is depicted by P_(CYL)(θ). Thetiming of combustion will vary from application to application. In thisparticular exemplary curve, P_(CYL)(θ) begins to rise from P_(MOT)(θ)around TDC, describing an ignition event sometime before TDC. As thecharge combusts, heat and work result from the combustion, resulting inan increase in pressure within the combustion chamber. PR is a ratio ofP_(MOT) to P_(CYL), and P_(MOT) is a component of P_(CYL). Netcombustion pressure (NCP(θ)) is the difference between P_(CYL)(θ) andP_(MOT)(θ) or the pressure rise in the combustion chamber attributableto combustion at a given crank angle. It will be appreciated that bysubtracting one from PR, a ratio of NCP to P_(MOT) may be determined.

$\begin{matrix}{{{P\;{R(\theta)}} - 1} = {{\frac{P_{CYL}(\theta)}{P_{MOT}(\theta)} - \frac{P_{MOT}(\theta)}{P_{MOT}(\theta)}} = \frac{N\; C\;{P(\theta)}}{P_{MOT}(\theta)}}} & \lbrack 16\rbrack\end{matrix}$PR measured through the equation above therefore may be used to directlydescribe the strength of combustion within a cylinder. Normalizing PRminus one at crank angle θ to an expected or theoretical maximum PRvalue minus one yields a fractional pressure ratio of the pressure risedue to combustion at crank angle θ to the expected total pressure risedue to combustion at the completion of the combustion process. Thisnormalization can be expressed by the following equation:

$\begin{matrix}{{F\; P\;{R(\theta)}} = {\frac{{P\;{R(\theta)}} - 1}{{P\;{R\left( {90{^\circ}} \right)}} - 1} \propto {{MassFractionBurn}(\theta)}}} & \lbrack 17\rbrack\end{matrix}$This fractional pressure ratio, by equating pressure rise attributableto combustion to the progression of combustion, describes the massfraction burn for that particular combustion process. By utilizing PRM,pressure readings from a cylinder may be used to estimate mass fractionburn for that cylinder.

The above method utilizing PRM is applicable for broad ranges oftemperature, cylinder charge and timings associated with compressionignition engines, with the added benefit of not requiring calibratedpressure sensors. Because PR is a ratio of pressures, a non-calibratedlinear pressure transducer may be utilized to acquire pressure datareadings from each cylinder.

Another method to estimate mass fraction burn is to directly utilize theRassweiler approach to determine mass fraction burn by calculating thetotal heat released for a given crank angle. The Rassweiler approachutilizes pressure readings from a cylinder to approximate theincremental heat release in the cylinder. This approach is given by thefollowing equation:

$\begin{matrix}{{Q_{Released}(\theta)} = {{\sum P_{k + 1}} - {P_{k - 1}\left( \frac{V_{k - 1}}{V_{k}} \right)}^{r}}} & \lbrack 18\rbrack\end{matrix}$Mass fraction burn, a measure of how much of the charge has beencombusted by a certain crank angle, may be approximated by determiningwhat fraction of heat release for a combustion process has taken placeat a given crank angle. The incremental heat release determined by theRassweiler approach may be summed over a range of crank angles, comparedto the total expected or theoretical heat release for the combustionprocess, and utilized to estimate mass fraction burn. For example, if75% of the total expected heat release has been realized for a givencrank angle, we can estimate that 75% of the combustion for the cyclehas taken place at that crank angle.

Other methods may be used to estimate mass fraction burn. One methodquantifies the rate of change of energy within the combustion chamberdue to combustion through an analysis of classical heat release measuresbased on analysis of the heat released and work performed through thecombustion of the charge. Such analyses are focused on the First Law ofThermodynamics, which states that the net change on energy in a closedsystem is equal to the sum of the heat and work added to the system.Applied to a combustion chamber, the energy increase in the combustionchamber and the enclosed gases equals the heat transferred to the wallsof the chamber and the gases plus the expansive work performed by thecombustion.

An exemplary method utilizing these classic heat release measures toapproximate a mass fraction burn estimate analyzes the rate of heatrelease by charge combustion throughout combustion process. This rate ofheat release, dQ_(ch)/dθ, may be integrated over a range of crank anglesin order to describe the net energy released in the form of heat.Through derivations known in the art, this heat release may be expressedthrough the following equation:

$\begin{matrix}{Q = {{\int\frac{\mathbb{d}Q_{ch}}{\mathbb{d}\theta}} = {\int\left( {{\frac{\gamma}{\gamma - 1}p\frac{\mathbb{d}V}{\mathbb{d}\theta}} + {\frac{1}{\gamma - 1}V\frac{\mathbb{d}p}{\mathbb{d}\theta}}} \right)}}} & \lbrack 19\rbrack\end{matrix}$Gamma, γ, comprises a ratio of specific heats and is nominally chosen asthat for air at the temperature corresponding to those used forcomputing the signal bias and without EGR. Thus, nominally or initiallyγ=1.365 for diesel engines and nominally γ=1.30 for conventionalgasoline engines. These can however be adjusted based on the data fromthe specific heats for air and stoichiometric products using an estimateof the equivalence ratio, φ, and EGR molar fraction targeted for theoperating condition and using the relation that [γ=1+(R/c_(v))], whereinR is the universal gas constant, and the weighted average of air andproduct properties through the expression:c _(v)(T)=(1.0−φ*EGR)*c _(vair)(T)+(φ*EGR)*c _(vstoichprod)(T)  [20]With the expression evaluated at the gas temperature corresponding tothat for pressures sampled for the computation of signal bias.

Whether calculated through the preceding method or by some other methodknown in the art, the calculation of energy released within thecombustion process for a given crank angle may be compared to anexpected or theoretical total energy release for the combustion process.This comparison yields an estimate of mass fraction burn for use indescribing combustion phasing.

The methods described hereinabove are readily reduced to be programmedinto a microcontroller or other device for execution during ongoingoperation of an internal combustion engine, as follows.

Once a mass fraction burn curve is generated for a particular combustionprocess, the curve is useful to evaluate the combustion phasing for thatparticular combustion process. Referring again to FIG. 7, a referencepoint is taken from which to compare mass fraction burn estimates fromdifferent combustion processes. In this particular embodiment, CA50%,representing the crank angle at which 50% of the charge is combusted, isselected. Other measures can be selected so long as the same measure isused for every comparison.

Determination of mass fraction burn values is a practice known in theart. Although exemplary methods are described above for determining massfraction burn, the methods disclosed herein to utilize mass fractionburn values to diagnose cylinder combustion issues may be used with anymethod to determine mass fraction burn. Any practice for developing massfraction burn may be utilized, and this disclosure is not intended to belimited to the specific methods described herein.

Additional methods exist to analyze cylinder pressure signals. Methodsare known for processing complex or noisy signals and reducing them touseful information. One such method includes spectrum analysis throughFast Fourier Transforms (FFT). FFTs reduce a periodic or repeatingsignal into a sum of harmonic signals useful to transform the signalinto the components of its frequency spectrum. Once the components ofthe signal have been identified, they may be analyzed and informationmay be taken from the signal.

Pressure readings from the pressure transducers located in or incommunication with the combustion cylinders contain information directlyrelated to the combustion occurring within the combustion chamber.However, engines are very complex mechanisms, and these pressurereadings can contain, in addition to a measure of P_(CYL)(θ), amultitude of pressure oscillations from other sources. Fast FourierTransforms (FFTs) are mathematical methods known in the art. One FFTmethod known as spectrum analysis analyzes a complex signal andseparates the signal into its component parts which may be representedas a sum of harmonics. Spectrum analysis of a pressure transducer signalrepresented by f(θ) may be represented as follows:FFT(f(θ)=A ₀+(A ₁ sin(ω₀θ+φ₁))+(A ₂ sin(2ω₀θ+φ₂))+ . . . +(A _(N) sin(Nω₀θ+φ_(N)))  [21]Each component N of the signal f(θ) represents a periodic input on thepressure within the combustion chamber, each increasing increment of Nincluding signals or higher frequency. Experimental analysis has shownthat the pressure oscillation caused by combustion and the piston movingthrough the various stages of the combustion process, P_(CYL)(θ), tendsto be the first, lowest frequency harmonic. By isolating this firstharmonic signal, P_(CYL)(θ) can be measured and evaluated. As is knownin the art, FFTs provide information regarding the magnitude and phaseof each identified harmonic, captured as the φ term in each harmonic ofthe above equation. The angle of first harmonic, or φ₁, is, therefore,the dominant term tracking combustion phasing information. By analyzingthe component of the FFT output related to P_(CYL), the phasinginformation of this component can be quantified and compared to eitherexpected phasing or the phasing of other cylinders. This comparisonallows for the measured phasing values to be evaluated and a warningindicated if the difference is greater than a threshold phasingdifference, indicating combustion issues in that cylinder.

Signals analyzed through FFTs are most efficiently estimated when theinput signal is at steady state. Transient effects of a changing inputsignal can create errors in the estimations performed. While methods areknown to compensate for the effects of transient input signals, themethods disclosed herein are best performed at either idle or steady,average engine speed conditions in which the effects of transients areeliminated. One known method to accomplish the test in an acceptablysteady test period is to take samples and utilize an algorithm withinthe control module to either validate or disqualify the test data asbeing taken during a steady period of engine operation.

It should be noted that although the test data is preferably taken atidle or steady engine operation, information derived from these analysescan be utilized by complex programmed calculations or engine models toeffect more accurate engine control throughout various ranges of engineoperation. For example, if testing and analysis at idle shows thatcylinder number four has a partially clogged injector, fuel injectiontiming could be modified for this cylinder throughout different rangesof operation to compensate for the perceived issue.

Once cylinder pressure signals have been analyzed through FFTs,information from the pressure signal can be used in variety of ways toanalyze the combustion process. For example, the analyzed pressuresignal can be used to generate a fractional pressure ratio as discussedin methods above and used to describe the mass fraction burn percentageto describe the progress of the combustion process.

Once a measure such as pressure readings are available, otherdescriptive parameters relating to a combustion process can becalculated. Sub-models describing particular characteristics of acombustion process can be employed utilizing physical characteristicsand relationships known in the art to translate cylinder pressures andother readily available engine sensor terms into variable descriptive ofthe combustion process. For example, volumetric efficiency, a ratio ofair-fuel charge entering the cylinder as compared to the capacity of thecylinder, can be expressed through the following equation:η_(VE) =f(RPM,P _(im) ,{dot over (m)} _(a))  [22]RPM, or engine speed, is easily measurable through a crankshaft speedsensor, as describe above. P_(im), or intake manifold pressure, istypically measured as related to engine control, and is a readilyavailable term. {dot over (m)}_(a)or the fresh mass air flow portion ofthe charge flowing into the cylinder, is also a term frequently measuredin the air intake system of the engine or can alternatively be easilyderived from P_(im), ambient barometric pressure, and knowncharacteristics of the air intake system. Another variable descriptiveof the combustion process that can be derived from cylinder pressuresand other readily available sensor readings is charge flow into thecylinder, {dot over (m)}_(c). {dot over (m)}_(c) can be determined bythe following equation:

$\begin{matrix}{{\overset{.}{m}}_{c} = \frac{P_{im} \cdot {rpm} \cdot D \cdot \eta}{2\;{RT}_{im}}} & \lbrack 23\rbrack\end{matrix}$D equals the displacement of the engine. R is a gas constant known inthe art. T_(im) is a temperature reading from the inlet manifold.Another variable descriptive of the combustion process that can bederived from cylinder pressures and other readily available sensorreadings is EGR %, or the percentage of exhaust gas being diverted intothe exhaust gas recirculation circuit. EGR % can be determined by thefollowing equation:

$\begin{matrix}{{E\; G\; R\mspace{14mu}\%} = {1 - \frac{{\overset{.}{m}}_{a}}{{\overset{.}{m}}_{c}}}} & \lbrack 24\rbrack\end{matrix}$Yet another variable descriptive of the combustion process that can bederived from cylinder pressures and other readily available sensorreadings is CAx, wherein x equals a desired fractional pressure ratio.CAx can be determined by the following equation, closely related toequation (2) above:

$\begin{matrix}{Z = {\frac{P_{CYL}(\theta)}{P_{MOT}(\theta)} - 1}} & \lbrack 25\rbrack\end{matrix}$Filling in the desired fractional pressure ratio as Z and solving for θyields CAx. For instance CA50 can be determined as the following:

$\begin{matrix}{\frac{P_{CYL}(\theta)}{P_{MOT}(\theta)} = 1.5} & \lbrack 26\rbrack\end{matrix}$Various temperatures within the combustion chamber can also be estimatedfrom cylinder pressures and other readily available sensor readings.FIG. 8 depicts a number of different temperatures capable of estimationwithin the combustion chamber important to describing the combustionprocess, in accordance with the present disclosure. T_(a), the averagetemperature within the combustion chamber can be determined by thefollowing equation:

$\begin{matrix}{T_{a} = \frac{P_{\max} \cdot {V({PPL})}}{1.05*{\overset{.}{m}}_{c}R}} & \lbrack 27\rbrack\end{matrix}$P_(max) is the maximum pressure achieved within the combustion chamberthrough the combustion process. PPL is a measure of the crank angle atwhich P_(max) occurs. V(PPL) is the volume of the cylinder at the pointP_(max) occurs. T_(u), the average temperature of the not yet combustedor unburned portion of the charge within the combustion chamber, can bedetermined by the following equation:

$\begin{matrix}{T_{u} = {{\frac{1.05*{\overset{.}{m}}_{c}}{{1.05*{\overset{.}{m}}_{c}} - {{\alpha \cdot {\overset{.}{m}}_{f}}\lambda_{s}}}\left\lbrack {{0.05\beta\; T_{ex}} + {0.95\; T_{im}}} \right\rbrack}\left( \frac{P_{\max} - {\Delta\; P}}{P_{im}} \right)^{\frac{r - 1}{r}}}} & \lbrack 28\rbrack\end{matrix}${dot over (m)}_(f) is the fuel mass flow, and can be determined eitherfrom a known fuel rail pressure in combination with known properties andoperation of the fuel injectors or from {dot over (m)}_(c) and {dot over(m)}_(α). α and β are calibrations based on engine speed and load andmay be developed experimentally, empirically, predictively, throughmodeling or other techniques adequate to accurately predict engineoperation, and a multitude of calibration curves might be used by thesame engine for each cylinder and for different engine settings,conditions, or operating ranges. λ_(S) is the stoichiometric air-fuelratio for the particular fuel and includes values known in the art.T_(ex) is a measured exhaust gas temperature. T_(im) and P_(im) aretemperature and pressure readings taken at the intake manifold.P_(max)−ΔP describes the pressure in the combustion chamber just beforethe start of combustion. γ is a specific heat constant described above.T_(b), the average temperature of the combusted or burned portion of thecharge within the combustion chamber, can be determined by the followingequation:

$\begin{matrix}{{T_{b} = \frac{T_{a} - {\left( {1 - x_{b}} \right)T_{u}}}{x_{b}}},{x_{b} = \frac{\alpha \cdot {{\overset{.}{m}}_{f}\left( {1 + \lambda_{S}} \right)}}{1.05{\overset{.}{m}}_{c}}}} & \lbrack 29\rbrack\end{matrix}$Note that the above equations are simplified in a method known in theart by neglecting heat loss to cylinder wall. Methods to compensate forthis simplification are known in the art and will not be described indetail herein. Through the use of the aforementioned relationships andderivations, cylinder pressure and other readily available sensorreadings can be used to determine a number of parameters descriptive ofthe combustion process being monitored.

As described above, cylinder pressure readings can be used to describe astate of combustion occurring within the combustion chamber for use as afactor in estimating NOx creation. Also as described above, a number ofother factors are important to accurately estimating NOx creation. FIG.9 is a graphical depiction of exemplary modeled results describingstandardized effects of a number of inputs to NOx emissions under agiven set of conditions, in accordance with the present disclosure. Asdescribed above, methods are known utilizing a model module and a NOxestimation module to simulate or estimate NOx creation based upon knowncharacteristics of an engine. The model utilized to characterize NOxcreation by a combustion process in this particular exemplary analysiscan be characterized by the following expression:NOx=NNT(Pmax,CA50,CAp max,EGR %,AFR)  [30]

As shown in the graphical results of FIG. 9, a number of factors havevarying effects on NOx creation. Under this particular set ofconditions, EGR % has the largest impact upon NOx creation for theengine modeled. In this instance, by methods known in the art,recirculating a particular amount of exhaust gas back into thecombustion chamber through the EGR circuit lowers the adiabatic flametemperature of the combustion process, thereby lowering the temperaturesthat nitrogen and oxygen molecules are exposed to during combustion and,thereby, lowering the rate of NOx creation. By studying such modelsunder various engine operating conditions, the neural network can beprovided with the most useful inputs to provide accurate estimates ofNOx creation. Additionally, studying such models provides informationuseful to selecting input data to initially train the neural network,varying inputs and providing corresponding outputs to sensor inputs anddescriptive parameters most likely to impact NOx creation.

By methods described above, NOx creation estimates can be generated fora set of engine sensor inputs. As will be appreciated by one havingordinary skill in the art, equations and model predictions of engineoperation frequently operate most effectively when the engine isoperating at or near steady state However, observations and predictionscan be made regarding the effects of transient or dynamic engineoperation upon NOx creation estimates or the accuracy thereof. Anexemplary expression describing a dynamic model or dynamic filteringmodule is shown by the following:

$\begin{matrix}{\frac{\mathbb{d}{NOx}}{\mathbb{d}t} = {f\left( {{NOx},y,{E\; G\; R\mspace{14mu}\%},{AFR},{Ta},{RPM}} \right)}} & \lbrack 31\rbrack\end{matrix}$wherein contemporary NOx readings and an output y from a trained neuralnetwork are utilized to estimate a change in NOx creation. Such a changevariable can be used to incrementally estimate NOx creation or can beused to check or filter NOx creation estimations. FIG. 14 schematicallydepicts an exemplary system generating a NOx creation estimate,utilizing models within a neural network to generate NOx creationestimates and including a dynamic model module to compensated NOxcreation estimates for the effects of dynamic engine and vehicleconditions, in accordance with the present disclosure. NOx creationestimate system 400 comprises a model module 410, a neural networkmodule 420, and a dynamic model module 430. Factors under currentoperating conditions most likely to impact NOx creation estimation underdynamic or changing conditions can be determined experimentally,empirically, predictively, through modeling or other techniques adequateto accurately predict engine operation. Inputs relating to these factorsare fed to dynamic model module 430 along with output from neuralnetwork module 420, and the raw output from the neural network can beadjusted, filtered, averaged, de-prioritized or otherwise modified basedupon the projected effects of the dynamic conditions determined bydynamic model module 430. In this way, the effects of dynamic engine orvehicle operation conditions can be accounted for in the estimation ofNOx creation.

As described above, integration can be used as a low pass filter in thecomparison of an actual conversion efficiency to a malfunctionconversion efficiency. FIG. 10 graphically illustrates exemplary data,comparing predicted NOx exiting an aftertreatment system generatedaccording to noisy input data, in accordance with the presentdisclosure. As is evident in the data plots, the data generated ischoppy with a number of spikes. Interpretation of the various signals,especially a comparison of the various predicted NOx values at any giventime, is prone to misinterpretation or false identifications. FIG. 11graphically illustrates exemplary data processed through an integrationcalculation, in accordance with the present disclosure. As is evident inthe data plots, comparison of the data curves generated throughintegration is greatly simplified, and the potential formisinterpretation or false identifications in a comparison are greatlyreduced.

The disclosure has described certain preferred embodiments andmodifications thereto. Further modifications and alterations may occurto others upon reading and understanding the specification. Therefore,it is intended that the disclosure not be limited to the particularembodiment(s) disclosed as the best mode contemplated for carrying outthis disclosure, but that the disclosure will include all embodimentsfalling within the scope of the appended claims.

1. Method for indicating a malfunctioning catalyst in a powertrainincluding an internal combustion engine and an aftertreatment systemhaving an aftertreatment device utilizing a catalyst to convert NOx, themethod comprising: monitoring an actual NOx content exiting theaftertreatment system; monitoring factors affecting conversionefficiency of the aftertreatment device; determining a predictedthreshold NOx content exiting the aftertreatment system for an exemplarymalfunctioning catalyst based upon the factors affecting conversionefficiency; comparing the actual NOx content exiting the aftertreatmentsystem to the predicted threshold NOx content exiting the aftertreatmentsystem; and indicating a malfunctioning catalyst based upon thecomparing; wherein monitoring the factors affecting conversionefficiency comprises: monitoring a NOx content entering theaftertreatment system; monitoring a bed temperature within theaftertreatment device; monitoring a space velocity within theaftertreatment device; and monitoring an amount of ammonia storagewithin the aftertreatment device.
 2. The method of claim 1, whereinmonitoring the NOx content entering the aftertreatment system comprisesoperating a virtual NOx sensor.
 3. The method of claim 1, furthercomprising warning an operator of the powertrain based upon theindicating.
 4. The method of claim 1, further comprising modulatingoperation of the powertrain based upon the indicating.
 5. The method ofclaim 4, wherein modulating operation of the powertrain comprisescommanding operation of the engine to create less NOx.
 6. The method ofclaim 4, wherein modulating operation of the powertrain comprisesoperating the aftertreatment system assuming decreased performance fromthe malfunctioning catalyst.
 7. Method for indicating a malfunctioningcatalyst in a powertrain including an internal combustion engine and anaftertreatment system having an aftertreatment device utilizing acatalyst to convert NOx, the method comprising: monitoring an actual NOxcontent exiting the aftertreatment system; monitoring factors affectingconversion efficiency of the aftertreatment device; determining apredicted threshold NOx content exiting the aftertreatment system for anexemplary malfunctioning catalyst based upon the factors affectingconversion efficiency; comparing the actual NOx content exiting theaftertreatment system to the predicted threshold NOx content exiting theaftertreatment system; and indicating a malfunctioning catalyst basedupon the comparing; wherein monitoring the actual NOx content exitingthe aftertreatment system comprises: monitoring a NOx sensor locateddownstream of the aftertreatment system; and determining the actual NOxcontent exiting the aftertreatment system based upon integrating datafrom the monitored NOx sensor located downstream of the aftertreatmentsystem through a time period; and wherein determining the predictedthreshold NOx content exiting the aftertreatment system for theexemplary malfunctioning catalyst comprises determining an instantaneouspredicted threshold NOx content exiting the aftertreatment system basedupon the factors affecting conversion efficiency, and determining thepredicted threshold NOx content exiting the aftertreatment system basedupon integrating instantaneous predicted threshold NOx content exitingthe aftertreatment system through the time period.
 8. Method forindicating a malfunctioning catalyst in a powertrain including aninternal combustion engine and an aftertreatment system having anaftertreatment device utilizing a catalyst to convert NOx, the methodcomprising: monitoring an actual NOx content exiting the aftertreatmentsystem; monitoring factors affecting conversion efficiency of theaftertreatment device; determining a predicted threshold NOx contentexiting the aftertreatment system for an exemplary malfunctioningcatalyst based upon the factors affecting conversion efficiency;comparing the actual NOx content exiting the aftertreatment system tothe predicted threshold NOx content exiting the aftertreatment system;and indicating a malfunctioning catalyst based upon the comparing;wherein determining the predicted threshold NOx content exiting theaftertreatment system for the exemplary malfunctioning catalystcomprises utilizing a look-up table.
 9. Method for indicating amalfunctioning catalyst in a powertrain including an internal combustionengine and an aftertreatment system having an aftertreatment deviceutilizing a catalyst to convert NOx, the method comprising: monitoringan actual NOx content exiting the aftertreatment system; monitoringfactors affecting conversion efficiency of the aftertreatment device;determining a predicted threshold NOx content exiting the aftertreatmentsystem for an exemplary malfunctioning catalyst based upon the factorsaffecting conversion efficiency; comparing the actual NOx contentexiting the aftertreatment system to the predicted threshold NOx contentexiting the aftertreatment system; and indicating a malfunctioningcatalyst based upon the comparing; wherein determining the predictedthreshold NOx content exiting the aftertreatment system for theexemplary malfunctioning catalyst comprises calculating the predictedthreshold NOx content exiting the aftertreatment system for theexemplary malfunctioning catalyst with a programmed functionalrelationship; wherein calculating the predicted threshold NOx contentexiting the aftertreatment system for the exemplary malfunctioningcatalyst with the programmed functional relationship comprises:determining a predicted nominal NOx content exiting the aftertreatmentsystem for an exemplary fresh catalyst based upon the factors affectingconversion efficiency of the aftertreatment device; and calculating thepredicted threshold NOx content exiting the aftertreatment system for anexemplary malfunctioning catalyst by dividing the predicted nominal NOxcontent exiting the aftertreatment system for the exemplary freshcatalyst by a calibratable threshold factor.
 10. The method of claim 9,wherein the calibratable threshold factor is based upon a space velocitywithin the aftertreatment device and a bed temperature within theaftertreatment device.
 11. Method for indicating a malfunctioningcatalyst in a powertrain including an internal combustion engine and anaftertreatment system having an aftertreatment device utilizing acatalyst to convert NOx, the method comprising: monitoring an actual NOxcontent exiting the aftertreatment system; monitoring factors affectingconversion efficiency of the aftertreatment device; determining apredicted nominal NOx content exiting the aftertreatment system for anexemplary fresh catalyst based upon the factors affecting conversionefficiency of the aftertreatment device; comparing the actual NOxcontent exiting the aftertreatment system and the predicted nominal NOxcontent exiting the aftertreatment system for the exemplary freshcatalyst; and indicating a malfunctioning catalyst if the actual NOxcontent exiting the aftertreatment system exceeds the predicted nominalNOx content exiting the aftertreatment system for the exemplary freshcatalyst by more than a threshold NOx content above nominal; wherein themonitoring factors affecting conversion efficiency comprises: monitoringa NOx content entering the aftertreatment system; monitoring a bedtemperature within the aftertreatment device; monitoring a spacevelocity within the aftertreatment device; and monitoring an amount ofammonia storage within the aftertreatment device.
 12. System forindicating a malfunctioning catalyst in a powertrain including aninternal combustion engine and an aftertreatment system having anaftertreatment device utilizing a catalyst to convert NOx, the systemcomprising: the aftertreatment device; a sensor located to detect NOxcontent present in an exhaust gas flow downstream of the aftertreatmentdevice; and a control module monitoring the sensor located to detect NOxcontent present in an exhaust gas flow downstream of the aftertreatmentdevice, monitoring factors affecting conversion efficiency of theaftertreatment device, determining a predicted threshold NOx contentexiting the aftertreatment system for an exemplary malfunctioningcatalyst based upon the factors affecting conversion efficiency,comparing data from the sensor located to detect NOx content present inan exhaust gas flow downstream of the aftertreatment device to thepredicted threshold NOx content exiting the aftertreatment system, andindicating the malfunctioning catalyst based upon the comparing; whereinthe control module determining the predicted threshold NOx contentexiting the aftertreatment system comprises utilizing a look-up table.13. The system of claim 12, the control module further generatingcommands to change operation of the engine based upon the indication ofthe malfunctioning catalyst.
 14. The system of claim 12, the controlmodule further generating commands to change operation of theaftertreatment system based upon the indication of the malfunctioningcatalyst.